Optical sorting by trajectory tracking with high sensitivity near the exceptional points

Exceptional points (EPs) in non-Hermitian systems embody abundant new physics and trigger various novel applications. In the optical force system, the motion of a particle near its equilibrium position is determined by the optical force stiffness matrix (OFSM), which is inherently non-Hermitian when the particle is illuminated by vortex beams. In this study, by exploiting the rapid variations in eigenvalues and the characteristics of particle motion near EPs of the OFSM, we propose a method to sort particles with subtle differences in their radii or refractive indices based on their trajectories in air. We demonstrate that the trajectory of a particle with parameters slightly larger than those corresponding to certain EPs closely resembles an ellipse. The increase in the major axis of the ellipse can be several orders of magnitude larger than the increase in particle radius. Furthermore, even a slight change in the refractive index can not only significantly alter the size of the ellipse but also rotate its orientation angle. Hence, particles with subtle differences can be distinguished by observing the significant disparities in their trajectories. This approach holds promise as a technique for the precise separation of micro and nanoscale particles.